US10311557B2 - Automated tonal balancing - Google Patents
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- US10311557B2 US10311557B2 US15/445,949 US201715445949A US10311557B2 US 10311557 B2 US10311557 B2 US 10311557B2 US 201715445949 A US201715445949 A US 201715445949A US 10311557 B2 US10311557 B2 US 10311557B2
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Definitions
- the disclosure relates to the field of image processing, and more particularly to the field of tonal balancing of ortho-rectified images for the sake of building a mosaic.
- the inventor has conceived and reduced to practice, in a preferred embodiment of the invention, a system and methods for automated tonal balancing that may operate regardless of the scale or quantity of images.
- the inventors For relative tonal balancing, the inventors have developed a way to hierarchically assemble an arbitrarily large number of images, dynamically grouping them based on a set of criteria (discussed below), tonally-balancing the images within a group, and then fusing those images together as a “super-image”. This process is then repeated, only now its the super-images are grouped together. This continues until there is a single “final image”. This method has been shown to work well using hundreds of images at once, both in terms of balancing quality and running time to complete.
- the inventors For global base-layer matching, the inventors have developed a way of tonally matching the images to a base layer in such a manner that adjacent or overlapping images appear tonally consistent.
- a system for automated tonal balancing comprising: a raw image database computer comprising program code stored in a memory and adapted to store and provide unmodified images and image information to other components of the system; a rectification server computer comprising program code stored in a memory and adapted to analyze and operate on input images to prepare them for tonal balancing, and to provide those images to other components of the system; a tone balancing server computer comprising program code stored in a memory and adapted to perform grouping and tone-balancing operations on sets of input images, and to provide the images and tone-balancing results to other components of the system; and a balanced image database computer comprising program code stored in a memory and adapted to store and provide tone-balanced images and image information to other components of the system, is disclosed.
- a method for performing tonal balancing on groups of images comprising the steps of: receiving, at a rectification server, a plurality of input images; classifying each of the images as an image group; performing, using a tone-balancing server, a grouping and balancing operation on the image groups; updating, using the rectification server, the input images with tone-balancing results; computing, using the tone-balancing server, an alternate tonal balance for remaining images; and providing the resulting balanced images as output, is disclosed.
- a method for assembling image groups that are internally tonally-balanced, into larger image groups that are internally tonally-balanced comprising the steps of: receiving, at a tone-balancing server, a plurality of input image groups, each of which is internally tonally-balanced; selecting an initial image group and making it the charter member of a new group; adding to the new group those input image groups that neighbor the initial group; tonally balancing the images in the new group; and adding the new group to a plurality of output image groups, is disclosed.
- FIG. 1 is a block diagram illustrating an exemplary hardware architecture of a computing device used in an embodiment of the invention.
- FIG. 2 is a block diagram illustrating an exemplary logical architecture for a client device, according to an embodiment of the invention.
- FIG. 3 is a block diagram showing an exemplary architectural arrangement of clients, servers, and external services, according to an embodiment of the invention.
- FIG. 4 is another block diagram illustrating an exemplary hardware architecture of a computing device used in various embodiments of the invention.
- FIG. 5 is a block diagram illustrating an exemplary system architecture for automated tonal balancing, according to a preferred embodiment of the invention.
- FIG. 6 is a flow diagram illustrating an exemplary method for performing tonal balancing on groups of images, according to a preferred embodiment of the invention.
- FIG. 7 is a flow diagram illustrating an exemplary method for grouping and balancing images, according to an embodiment of the invention.
- FIG. 8 is a flow diagram illustrating an exemplary local tonal balancing method, according to another embodiment of the invention.
- Devices that are in communication with each other need not be in continuous communication with each other, unless expressly specified otherwise.
- devices that are in communication with each other may communicate directly or indirectly through one or more communication means or intermediaries, logical or physical.
- steps may be performed simultaneously despite being described or implied as occurring non-simultaneously (e.g., because one step is described after the other step).
- the illustration of a process by its depiction in a drawing does not imply that the illustrated process is exclusive of other variations and modifications thereto, does not imply that the illustrated process or any of its steps are necessary to one or more of the invention(s), and does not imply that the illustrated process is preferred.
- steps are generally described once per embodiment, but this does not mean they must occur once, or that they may only occur once each time a process, method, or algorithm is carried out or executed. Some steps may be omitted in some embodiments or some occurrences, or some steps may be executed more than once in a given embodiment or occurrence.
- the techniques disclosed herein may be implemented on hardware or a combination of software and hardware. For example, they may be implemented in an operating system kernel, in a separate user process, in a library package bound into network applications, on a specially constructed machine, on an application-specific integrated circuit (ASIC), or on a network interface card.
- ASIC application-specific integrated circuit
- Software/hardware hybrid implementations of at least some of the embodiments disclosed herein may be implemented on a programmable network-resident machine (which should be understood to include intermittently connected network-aware machines) selectively activated or reconfigured by a computer program stored in memory.
- a programmable network-resident machine which should be understood to include intermittently connected network-aware machines
- Such network devices may have multiple network interfaces that may be configured or designed to utilize different types of network communication protocols.
- a general architecture for some of these machines may be described herein in order to illustrate one or more exemplary means by which a given unit of functionality may be implemented.
- At least some of the features or functionalities of the various embodiments disclosed herein may be implemented on one or more general-purpose computers associated with one or more networks, such as for example an end-user computer system, a client computer, a network server or other server system, a mobile computing device (e.g., tablet computing device, mobile phone, smartphone, laptop, or other appropriate computing device), a consumer electronic device, a music player, or any other suitable electronic device, router, switch, or other suitable device, or any combination thereof.
- at least some of the features or functionalities of the various embodiments disclosed herein may be implemented in one or more virtualized computing environments (e.g., network computing clouds, virtual machines hosted on one or more physical computing machines, or other appropriate virtual environments).
- Computing device 100 may be, for example, any one of the computing machines listed in the previous paragraph, or indeed any other electronic device capable of executing software- or hardware-based instructions according to one or more programs stored in memory.
- Computing device 100 may be adapted to communicate with a plurality of other computing devices, such as clients or servers, over communications networks such as a wide area network a metropolitan area network, a local area network, a wireless network, the Internet, or any other network, using known protocols for such communication, whether wireless or wired.
- communications networks such as a wide area network a metropolitan area network, a local area network, a wireless network, the Internet, or any other network, using known protocols for such communication, whether wireless or wired.
- computing device 100 includes one or more central processing units (CPU) 102 , one or more interfaces 110 , and one or more busses 106 (such as a peripheral component interconnect (PCI) bus).
- CPU 102 may be responsible for implementing specific functions associated with the functions of a specifically configured computing device or machine.
- a computing device 100 may be configured or designed to function as a server system utilizing CPU 102 , local memory 101 and/or remote memory 120 , and interface(s) 110 .
- CPU 102 may be caused to perform one or more of the different types of functions and/or operations under the control of software modules or components, which for example, may include an operating system and any appropriate applications software, drivers, and the like.
- CPU 102 may include one or more processors 103 such as, for example, a processor from one of the Intel, ARM, Qualcomm, and AMD families of microprocessors.
- processors 103 may include specially designed hardware such as application-specific integrated circuits (ASICs), electrically erasable programmable read-only memories (EEPROMs), field-programmable gate arrays (FPGAs), and so forth, for controlling operations of computing device 100 .
- ASICs application-specific integrated circuits
- EEPROMs electrically erasable programmable read-only memories
- FPGAs field-programmable gate arrays
- a local memory 101 such as non-volatile random access memory (RAM) and/or read-only memory (ROM), including for example one or more levels of cached memory
- RAM non-volatile random access memory
- ROM read-only memory
- Memory 101 may be used for a variety of purposes such as, for example, caching and/or storing data, programming instructions, and the like. It should be further appreciated that CPU 102 may be one of a variety of system-on-a-chip (SOC) type hardware that may include additional hardware such as memory or graphics processing chips, such as a Qualcomm SNAPDRAGONTM or Samsung EXYNOSTM CPU as are becoming increasingly common in the art, such as for use in mobile devices or integrated devices.
- SOC system-on-a-chip
- processor is not limited merely to those integrated circuits referred to in the art as a processor, a mobile processor, or a microprocessor, but broadly refers to a microcontroller, a microcomputer, a programmable logic controller, an application-specific integrated circuit, and any other programmable circuit.
- interfaces 110 are provided as network interface cards (NICs).
- NICs control the sending and receiving of data packets over a computer network; other types of interfaces 110 may for example support other peripherals used with computing device 100 .
- the interfaces that may be provided are Ethernet interfaces, frame relay interfaces, cable interfaces, DSL interfaces, token ring interfaces, graphics interfaces, and the like.
- interfaces may be provided such as, for example, universal serial bus (USB), Serial, Ethernet, FIREWIRETM, THUNDERBOLTTM, PCI, parallel, radio frequency (RF), BLUETOOTHTM, near-field communications (e.g., using near-field magnetics), 802.11 (WiFi), frame relay, TCP/IP, ISDN, fast Ethernet interfaces, Gigabit Ethernet interfaces, Serial ATA (SATA) or external SATA (ESATA) interfaces, high-definition multimedia interface (HDMI), digital visual interface (DVI), analog or digital audio interfaces, asynchronous transfer mode (ATM) interfaces, high-speed serial interface (HSSI) interfaces, Point of Sale (POS) interfaces, fiber data distributed interfaces (FDDIs), and the like.
- USB universal serial bus
- RF radio frequency
- BLUETOOTHTM near-field communications
- near-field communications e.g., using near-field magnetics
- WiFi wireless FIREWIRETM
- Such interfaces 110 may include physical ports appropriate for communication with appropriate media. In some cases, they may also include an independent processor (such as a dedicated audio or video processor, as is common in the art for high-fidelity A/V hardware interfaces) and, in some instances, volatile and/or non-volatile memory (e.g., RAM).
- an independent processor such as a dedicated audio or video processor, as is common in the art for high-fidelity A/V hardware interfaces
- volatile and/or non-volatile memory e.g., RAM
- FIG. 1 illustrates one specific architecture for a computing device 100 for implementing one or more of the inventions described herein, it is by no means the only device architecture on which at least a portion of the features and techniques described herein may be implemented.
- architectures having one or any number of processors 103 may be used, and such processors 103 may be present in a single device or distributed among any number of devices.
- a single processor 103 handles communications as well as routing computations, while in other embodiments a separate dedicated communications processor may be provided.
- different types of features or functionalities may be implemented in a system according to the invention that includes a client device (such as a tablet device or smartphone running client software) and server systems (such as a server system described in more detail below).
- the system of the present invention may employ one or more memories or memory modules (such as, for example, remote memory block 120 and local memory 101 ) configured to store data, program instructions for the general-purpose network operations, or other information relating to the functionality of the embodiments described herein (or any combinations of the above).
- Program instructions may control execution of or comprise an operating system and/or one or more applications, for example.
- Memory 120 or memories 101 , 120 may also be configured to store data structures, configuration data, encryption data, historical system operations information, or any other specific or generic non-program information described herein.
- At least some network device embodiments may include nontransitory machine-readable storage media, which, for example, may be configured or designed to store program instructions, state information, and the like for performing various operations described herein.
- nontransitory machine-readable storage media include, but are not limited to, magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROM disks; magneto-optical media such as optical disks, and hardware devices that are specially configured to store and perform program instructions, such as read-only memory devices (ROM), flash memory (as is common in mobile devices and integrated systems), solid state drives (SSD) and “hybrid SSD” storage drives that may combine physical components of solid state and hard disk drives in a single hardware device (as are becoming increasingly common in the art with regard to personal computers), memristor memory, random access memory (RAM), and the like.
- ROM read-only memory
- flash memory as is common in mobile devices and integrated systems
- SSD solid state drives
- hybrid SSD hybrid SSD
- such storage means may be integral and non-removable (such as RAM hardware modules that may be soldered onto a motherboard or otherwise integrated into an electronic device), or they may be removable such as swappable flash memory modules (such as “thumb drives” or other removable media designed for rapidly exchanging physical storage devices), “hot-swappable” hard disk drives or solid state drives, removable optical storage discs, or other such removable media, and that such integral and removable storage media may be utilized interchangeably.
- swappable flash memory modules such as “thumb drives” or other removable media designed for rapidly exchanging physical storage devices
- hot-swappable hard disk drives or solid state drives
- removable optical storage discs or other such removable media
- program instructions include both object code, such as may be produced by a compiler, machine code, such as may be produced by an assembler or a linker, byte code, such as may be generated by for example a JavaTM compiler and may be executed using a Java virtual machine or equivalent, or files containing higher level code that may be executed by the computer using an interpreter (for example, scripts written in Python, Perl, Ruby, Groovy, or any other scripting language).
- object code such as may be produced by a compiler
- machine code such as may be produced by an assembler or a linker
- byte code such as may be generated by for example a JavaTM compiler and may be executed using a Java virtual machine or equivalent
- files containing higher level code that may be executed by the computer using an interpreter (for example, scripts written in Python, Perl, Ruby, Groovy, or any other scripting language).
- systems according to the present invention may be implemented on a standalone computing system.
- FIG. 2 there is shown a block diagram depicting a typical exemplary architecture of one or more embodiments or components thereof on a standalone computing system.
- Computing device 200 includes processors 210 that may run software that carry out one or more functions or applications of embodiments of the invention, such as for example a client application 230 .
- Processors 210 may carry out computing instructions under control of an operating system 220 such as, for example, a version of Microsoft's WINDOWSTM operating system, Apple's Mac OS/X or iOS operating systems, some variety of the Linux operating system, Google's ANDROIDTM operating system, or the like.
- an operating system 220 such as, for example, a version of Microsoft's WINDOWSTM operating system, Apple's Mac OS/X or iOS operating systems, some variety of the Linux operating system, Google's ANDROIDTM operating system, or the like.
- one or more shared services 225 may be operable in system 200 , and may be useful for providing common services to client applications 230 .
- Services 225 may for example be WINDOWSTM services, user-space common services in a Linux environment, or any other type of common service architecture used with operating system 210 .
- Input devices 270 may be of any type suitable for receiving user input, including for example a keyboard, touchscreen, microphone (for example, for voice input), mouse, touchpad, trackball, or any combination thereof.
- Output devices 260 may be of any type suitable for providing output to one or more users, whether remote or local to system 200 , and may include for example one or more screens for visual output, speakers, printers, or any combination thereof.
- Memory 240 may be random-access memory having any structure and architecture known in the art, for use by processors 210 , for example to run software.
- Storage devices 250 may be any magnetic, optical, mechanical, memristor, or electrical storage device for storage of data in digital form (such as those described above, referring to FIG. 1 ). Examples of storage devices 250 include flash memory, magnetic hard drive, CD-ROM, and/or the like.
- systems of the present invention may be implemented on a distributed computing network, such as one having any number of clients and/or servers.
- FIG. 3 there is shown a block diagram depicting an exemplary architecture 300 for implementing at least a portion of a system according to an embodiment of the invention on a distributed computing network.
- any number of clients 330 may be provided.
- Each client 330 may run software for implementing client-side portions of the present invention; clients may comprise a system 200 such as that illustrated in FIG. 2 .
- any number of servers 320 may be provided for handling requests received from one or more clients 330 .
- Clients 330 and servers 320 may communicate with one another via one or more electronic networks 310 , which may be in various embodiments any of the Internet, a wide area network, a mobile telephony network (such as CDMA or GSM cellular networks), a wireless network (such as WiFi, Wimax, LTE, and so forth), or a local area network (or indeed any network topology known in the art; the invention does not prefer any one network topology over any other).
- Networks 310 may be implemented using any known network protocols, including for example wired and/or wireless protocols.
- servers 320 may call external services 370 when needed to obtain additional information, or to refer to additional data concerning a particular call. Communications with external services 370 may take place, for example, via one or more networks 310 .
- external services 370 may comprise web-enabled services or functionality related to or installed on the hardware device itself. For example, in an embodiment where client applications 230 are implemented on a smartphone or other electronic device, client applications 230 may obtain information stored in a server system 320 in the cloud or on an external service 370 deployed on one or more of a particular enterprise's or user's premises.
- clients 330 or servers 320 may make use of one or more specialized services or appliances that may be deployed locally or remotely across one or more networks 310 .
- one or more databases 340 may be used or referred to by one or more embodiments of the invention. It should be understood by one having ordinary skill in the art that databases 340 may be arranged in a wide variety of architectures and using a wide variety of data access and manipulation means.
- one or more databases 340 may comprise a relational database system using a structured query language (SQL), while others may comprise an alternative data storage technology such as those referred to in the art as “NoSQL” (for example, Hadoop Cassandra, Google BigTable, and so forth).
- SQL structured query language
- variant database architectures such as column-oriented databases, in-memory databases, clustered databases, distributed databases, or even flat file data repositories may be used according to the invention. It will be appreciated by one having ordinary skill in the art that any combination of known or future database technologies may be used as appropriate, unless a specific database technology or a specific arrangement of components is specified for a particular embodiment herein. Moreover, it should be appreciated that the term “database” as used herein may refer to a physical database machine, a cluster of machines acting as a single database system, or a logical database within an overall database management system.
- security and configuration management are common information technology (IT) and web functions, and some amount of each are generally associated with any IT or web systems. It should be understood by one having ordinary skill in the art that any configuration or security subsystems known in the art now or in the future may be used in conjunction with embodiments of the invention without limitation, unless a specific security 360 or configuration system 350 or approach is specifically required by the description of any specific embodiment.
- FIG. 4 shows an exemplary overview of a computer system 400 as may be used in any of the various locations throughout the system. It is exemplary of any computer that may execute code to process data. Various modifications and changes may be made to computer system 400 without departing from the broader scope of the system and method disclosed herein.
- CPU 401 is connected to bus 402 , to which bus is also connected memory 403 , nonvolatile memory 404 , display 407 , I/O unit 408 , and network interface card (NIC) 413 .
- I/O unit 408 may, typically, be connected to keyboard 409 , pointing device 410 , hard disk 412 , and real-time clock 411 .
- NIC 413 connects to network 414 , which may be the Internet or a local network, which local network may or may not have connections to the Internet. Also shown as part of system 400 is power supply unit 405 connected, in this example, to ac supply 406 . Not shown are batteries that could be present, and many other devices and modifications that are well known but are not applicable to the specific novel functions of the current system and method disclosed herein.
- functionality for implementing systems or methods of the present invention may be distributed among any number of client and/or server components.
- various software modules may be implemented for performing various functions in connection with the present invention, and such modules may be variously implemented to run on server and/or client components.
- FIG. 5 is a block diagram illustrating an exemplary system architecture 500 for automated tonal balancing, according to a preferred embodiment of the invention.
- a raw image database 501 may be a computing device comprising program code stored in a memory and adapted to store and provide data to other components of the system 500 , and may be connected to or in communication with (such as over a data packet network, or via a direct physical connection, for example) a rectification server 502 that may be a computing device comprising program code stored in a memory and adapted to perform image processing functions according to the invention, such as described below (referring to FIG. 6 and FIG. 7 ).
- a tone balancing server 503 may be a computing device comprising program code stored in a memory and adapted to process image data received from a rectification server 502 for tonal correction, such as described below (again, referring to FIGS. 6-7 ).
- a system 500 may further comprise a plurality of output devices 510 such as (for example) a display screen 511 that may provide image data for viewing or interaction by a human user, and a balanced image database 512 that may store tonally-balanced images provided by other components of the system 500 .
- FIG. 6 is a flow diagram illustrating an exemplary method 600 for performing tonal balancing on groups of images, according to a preferred embodiment of the invention.
- a rectification server may receive input imagery such as from a database or other image source.
- the server may initialize the imagery by setting each image as a “group”, for later use.
- a tone-balancing server may perform tonal balancing on the image groups (which at this point may consist of only individual images), by running a GROUP THE GROUPS operation as described below (referring to FIG. 7 ).
- a next step 604 the output of the operation may then be used by the rectification server to update images in the groups with the tonal-balancing results, producing a set of new, tonally-balanced groups.
- operation may continue in this fashion as needed (repeating from a previous step 603 ), until either a single group is left or a plurality of groups remain that cannot be tonally-balanced due to having ill-suited image overlaps to tonally-balance against.
- the remaining groups may be processed by the tone-balancing server using an alternate tonal balance operation, and in a final step 607 the results may be output such as for review or interaction by a human user, or for storage such as in a balanced image database.
- FIG. 7 is a flow diagram illustrating an exemplary method 700 for grouping and balancing images, according to an embodiment of the invention.
- the method illustrated may be used as a GROUP THE GROUPS operation as described previously, for such purposes as a multi-step tonal-matching operation over a plurality of images.
- a tone-balancing server may receive a plurality of input images, and in a next step 702 may select an image group A from the input.
- the server may then add the images of A to a new group B, and remove them from the input set.
- a next step 704 the server may then examine neighboring groups around A, and if they have overlapping areas deemed to be suitable to tonally-balance, may add those images to Band remove them from the input set.
- the server may then run tonal balancing operations on group B.
- the server may add B to the output set, along with the results of tonal-balancing.
- the server may iterate over the rest of the input set as above, grouping images and balancing them in a looping fashion continuing from a prior step 702 , and in a final step 708 when input is empty, output the images and tone-balancing results.
- the overlap between two groups of images may be ill-suited to tonal balancing.
- an algorithm referred to above as “ALTERNATIVE TONAL BALANCE” may be used.
- the ALTERNATIVE TONAL BALANCE algorithm may be one that is specifically designed to better handle such cases mentioned above, and may help alleviate the problem of poor results just described.
- FIG. 8 is a method flow diagram illustrating an exemplary local tonal balancing method 800 , according to another embodiment of the invention.
- local tonal balancing may take as input a plurality of imagery and apply functions to the pixels to map the input to that of a reference image that covers a particular area of interest (AOI) for which a mosaic should be produced.
- AOI area of interest
- a tone balancing server may divide an input image (that is, an image portion or slice that requires tonal matching, for example image slices received from a rectification server as described previously with reference to FIG. 5 ) into smaller portions or image patches (possibly overlapping as needed).
- a tone balancing server may create a function that maps the input pixel values (that is, the values of pixels within the initial input image) to output pixel values such that statistics (such as mean value per band or other image statistics) of an output patch match those of a reference image within a corresponding region—for example, such that an output patch corresponding to a city block matches the values of a reference image for that city block, the reference image being an unmodified image of an entire city or other large region encompassing at least the region within an image patch being processed.
- produced functions may then be aggregated into a global function that may be applied to an entire input image, such that the global function creates an output image that closely resembles a reference image.
- Such aggregation may be done, for example, by interpolation of the individual functions defined within a plurality of image patches defined previously, to create a smooth mapping of input values to output values (such that any seam lines or harsh transitions between patches or images may be minimized, giving the appearance of a continuous smooth transition).
- each input image may then be matched to a reference image independently of any other input images, facilitating a parallel operation that can process a large number of individual input images efficiently. Since the input images may be matched to the same reference image, the output images will necessarily have very similar tonal qualities such as color, due to aggregation of the input images as described above. This may be used to produce a large image mosaic from a number of input images, where the output mosaic has the appearance of a single image after processing (that is, when the images are “stitched” together) due to the smooth transitions between image portions produced by a local tonal matching process.
- any original data may be unmodified and preserved, while intermediate updates are accomplished by updating current tonal-balancing scaling values, and updated pixel values are derived on-the-fly.
- an original copy may be retained for comparison or future use, such as for re-processing using new or updated algorithms, for example.
- a global base-layer matching process may utilize an available ortho-rectified reference base-layer (for example, low-resolution Landsat 8 imagery) covering an area of interest.
- an available ortho-rectified reference base-layer for example, low-resolution Landsat 8 imagery
- images A and B may be locally tonally-matched to a base-layer so as to yield good tonal balance with respect to one another. It may be appreciated that such a process may then be generalized to all the input images (that is, the entirety of a plurality of input images of which only a portion may be comprised by images A and B).
- Local tonal matching is distinct from global tonal matching as described above, and it should be appreciated that each process may be carried out interchangeably, simultaneously, or in sequence according to a particular arrangement or use.
- one (gain, bias)-combination per image band may be prescribed to achieve a histogram match of an entire image band to a corresponding base-layer band (a portion covering the same visual area).
- f(col, row) per image band there is a function f(col, row) per image band that may be used to prescribe a local (gain, bias)-combination to achieve a local histogram match of an image band to a corresponding base-layer band.
- Image A may be subdivided into rectangular tiles.
- image B may also be subdivided into tiles. Where image B does overlap image A, image B may adopt image A's tiling. Each tile T of image A may then be matched to a corresponding tile area in the base-layer, and similarly to a previous image overlap process, tiles that overlap may inherit previous subdivided tile portions, and tiles that do not overlap may be subdivided accordingly. Similar overlap-and-inherit operations may be performed for various properties and values, wherein a property for an image B may inherit from a similar property of image A if there is overlap, and may be independently established for image B if there is no overlap.
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